Perturbed decoder, perturbed decoding method and apparatus in communication system using the same

ABSTRACT

A decoder adopted to receive a signal transmitted in a communication system, includes one or more of a module adopted to pre-process a received signal to reduce the effect of interference-plus-noise on the received signal before filtering the received signal, and a module adopted to post-process the result of filtering the received signal.

TECHNICAL FIELD

Apparatuses, methods and/or systems consistent with the followingdescription relate to a decoder, decoding method and an apparatus in acommunication system using the same, and more particularly, thedescription relates to a perturbed decoder, perturbed decoding methodand an apparatus in a multiple-input multiple-output (MIMO) wirelesssystem using the same.

BACKGROUND

MIMO wireless systems are known to provide considerable gains in datarates and diversity advantage over single antenna systems. Effectivedecoders are needed for multi-antenna systems that operate at these highdata rates. Taking full advantage of the optimal performance in MIMOsystems usually requires the use of a maximum-likelihood (ML) decoding.However, the complexity of the optimum ML decoder grows exponentiallywith the number of transmit antennas and the symbol constellation size.Accordingly, there has been a need for decoders that achieve areasonable trade-off between complexity and performance.

Some of the decoders that tried to achieve this trade-off attempt tomodify an initial estimate of a transmit symbol vector, for example inspace-time chase decoding and list-sphere decoding. The space-timechasing decoding is described, e.g., in D. J. Love, S. Hosur, A. Batraand R. W. Heath, “Space-time chase decoding,” IEEE Trans. on WirelessComm., 4(5):2035-2039, 2005 (Love et al.), and the list-sphere decodingis described, e.g., in B. Hochwald and S. T. Brink, “Achievingnear-capacity on a multiple-antenna channel,” IEEE Trans. Comm.,51:389{399, March 2002 (Hochwald et al.) and in B. Hassibi and B.Hochwald, “High rate codes that are linear in space and time,” IEEETransactions on Information Theory, 48(7):1804-1824, July 2002 (Hassibiet al.). These references are incorporated herein by reference in itsentirety for all purposes. These decoders may be considered asperforming some sort of post-processing on a filtered received symbolvector.

In space-time chase decoding in Love et al., it was shown that there isan improvement in performance of a zero-forcing (ZF) decoder with theaddition of space-time chase decoding techniques. A list sphere decoder(LSD) in Hochwald et al. and/or Hassibi et al. attempts to search forthe ML estimate by considering only transmit symbol vectors that arewithin a radius from a ZF estimate. The limitations and drawbacks of theLSD are based on the aspect that the performance is dependent on thesearch radius. Moreover, it may not be considered in a multiuserscenario.

Accordingly, there is a need for new decoders, decoding methods, andapparatuses and systems using the same.

SUMMARY

According to an aspect, there is provided a decoder which perturbs theresult of filtering a received signal. The decoder may be referred toas, for example, a post-perturbed decoder. The decoder may be used in asingle-user MIMO (SU-MIMO) scenario where a spatial diversitymultiplexing (SDM) is used to transmit multiple streams to a singleuser. The decoder may be used in a multiple-user MIMO (MU-MIMO) scenariowhere a spatial diversity multiple access (SDMA) is used to transmitmultiple streams to multiple users simultaneously. The decoder mayimprove the performance of linear decoders such as ZF and minimum meansquare error (MMSE) decoders by perturbing the result of filtering thereceived signal. The decoder may create a list of possible transmitsymbol vector candidates. With the list, a hard decision decoding may beperformed on transmit symbol vectors or a soft decision decoding may beperformed for transmitted bits. An outer channel code may be used forincreased performance.

According to another aspect, there is provided a decoder which reducesthe effects of interference-plus-noise at the decoder before decoding bypre-processing to reduce the effects of interference-plus-noise on areceived signal before decoding. The decoder may be referred to as, forexample, a pre-perturbed decoder. The decoder may reduce the effects ofinterference-plus-noise on transmitted symbols by perturbing a receivedsignal before filtering the received signal using. The filtering may beby way of linear decoding. The decoder may be used in multi-antennasystems. With the decoder, a hard decision decoding may be performed ontransmit symbol vectors or a soft decision decoding may be performed fortransmitted bits. An outer channel code may be used for increasedperformance.

According to still another aspect, there is provided a decoder whichpre-perturbs a received signal and post-perturbs an estimate fromfiltering the received signal. The decoder may be referred to as, forexample, a dual-perturbed decoder. The decoder may be used in a SU-MIMOscenario where a SDM is used to transmit multiple streams to a singleuser. The decoder may be used in a MU-MIMO scenario where a SDMA is usedto transmit multiple streams to multiple users simultaneously. Thedecoder may create a list of possible transmit symbol vector candidates.With the list, a hard decision decoding may be performed on transmitsymbol vectors or a soft decision decoding may be performed fortransmitted bits. An outer channel code may be used for increasedperformance.

According to still another aspect, there is provided a decoder adoptedto receive a signal transmitted in a communication system, the decodercomprising a module adopted to provide perturbation vectors, and amodule adopted to provide transmit symbol vector candidates byperturbing an estimate of a transmit symbol vector with the perturbationvectors.

The communication system may be a multiple-input multiple-output (MIMO)communication system.

The perturbation vectors may be randomly generated vectors that, onaverage, are contained within a sphere around the estimate.

The perturbation vectors may be individually added to the estimate andthe result mapped to provide the transmit symbol vector candidates.

The decoder may further comprise a module adopted to provide theestimate of the transmit symbol vector by filtering a received vector.

The module adopted to provide the transmit symbol vector candidates maycomprises a module adopted to provide transmit symbol vector estimatesby individually adding the perturbation vectors to the estimate and amodule adopted to provide the transmit symbol vector candidates bymapping the transmit symbol vector estimates to a constellation symbol.

The decoder may further comprise a module adopted to perform a harddecision decoding based on the transmit symbol vector candidates and/ora module adopted to perform a soft decision decoding for received bitsbased on the transmit symbol vector candidates. The decoder may beadopted to use an outer channel code.

The number of the transmit symbol vector candidates may be less thanthat of the perturbation vectors.

According to still another aspect, there is provided a decoder adoptedto receive a signal transmitted in a communication system, the decodercomprising a module adopted to provide perturbation vectors, and amodule adopted to provide processed received vectors by perturbing areceived vector with the perturbation vectors.

The perturbation vectors may be randomly generated vectors having astatistical nature corresponding to interference-plus-noise on thereceived vector.

The perturbation vectors may be individually added to the receivedvector to provide the processed received vectors.

The decoder may further comprise a module adopted to provide transmitsymbol vector estimates by filtering the processed received vectors. Thedecoder may further comprise a module adopted to provide transmit symbolvector candidates by mapping the transmit symbol vector estimates to aconstellation symbol. The decoder may further comprise a module adoptedto perform a hard decision decoding based on the transmit symbol vectorcandidates and/or a module adopted to perform a soft decision decodingfor received bits based on the transmit symbol vector candidates.

The decoder may further comprise a module adopted to provide transmitsymbol vector candidates by perturbing at least a subset of the transmitsymbol vector estimates with post-perturbation vectors. Thepost-perturbation vectors may be randomly generated vectors that, onaverage, are contained within a sphere around a transmit symbol vectorestimate.

The at least the subset of the transmit symbol vector estimates may beindividually added to the post-perturbation vectors and the resultmapped to provide the transmit symbol vector candidates.

The module adopted to provide the transmit symbol vector candidates maycomprises a module adopted to provide post-transmit symbol vectorestimates by individually adding the at least the subset of the transmitsymbol vector estimates to the post-perturbation vectors and a moduleadopted to provide the transmit symbol vector candidates by mapping thepost-transmit symbol vector estimates to a constellation symbol.

According to still another aspect, there is provided a decoder adoptedto receive a signal transmitted in a multiple-input multiple-output(MIMO) communication system, the decoder comprising one or more of amodule adopted to pre-process a received signal to reduce the effect ofinterference-plus-noise on the received signal before filtering thereceived signal, and a module adopted to post-process the result offiltering the received signal. The module adopted to post-processprovides transmit symbol vector candidates by perturbing the result withperturbation vectors.

According to still another aspect, there is provided an apparatus forreceiving and/or transmitting a signal in a communication system, theapparatus comprising a detector, and a decoder adopted to providetransmit symbol vector candidates by perturbing an estimate of atransmit symbol vector with perturbation vectors.

The perturbation vectors may be randomly generated vectors that, onaverage, are contained within a sphere around the estimate.

The perturbation vectors may be individually added to the estimate andthe result mapped to provide the transmit symbol vector candidates.

The decoder may obtain the estimate of the transmit symbol vectorprovided by filtering a received vector.

According to still another aspect, there is provided an apparatus forreceiving and/or transmitting a signal in a communication system, theapparatus comprising a detector, and a decoder adopted to provideprocessed received vectors by perturbing a received vector withperturbation vectors.

The perturbation vectors may be randomly generated vectors having astatistical nature corresponding to interference-plus-noise on thereceived vector.

The perturbation vectors may be individually added to the receivedvector to provide the processed received vectors.

The decoder may obtain transmit symbol vector estimates provided byfiltering the processed received vectors.

The decoder may provide transmit symbol vector candidates by mapping thetransmit symbol vector estimates to a constellation symbol.

The decoder may be adopted to provide transmit symbol vector candidatesby perturbing at least a subset of the transmit symbol vector estimateswith post-perturbation vectors. The post-perturbation vectors may berandomly generated vectors that, on average, are contained within asphere around a transmit symbol vector estimate. The at least the subsetof the transmit symbol vector estimates may be individually added to thepost-perturbation vectors and the result mapped to provide the transmitsymbol vector candidates.

According to still another aspect, there is provided an apparatus forreceiving and/or transmitting a signal in a multiple-inputmultiple-output (MIMO) communication system, the apparatus comprising adetector, and a decoder comprising one or more of a module adopted topre-process a received signal to reduce the effect ofinterference-plus-noise on the received signal before filtering thereceived signal, and a module adopted to post-process the result offiltering the received signal. The module adopted to post-process mayprovide transmit symbol vector candidates by perturbing the result withperturbation vectors.

According to still another aspect, there is provided a method for use inan apparatus adopted to receive a signal transmitted in a communicationsystem, the method comprising generating perturbation vectors, andgenerating transmit symbol vector candidates by perturbing an estimateof a transmit symbol vector with the perturbation vectors.

The generating of the perturbation vectors may comprise randomlygenerating vectors that, on average, are contained within a spherearound the estimate.

The generating of the transmit symbol vector candidates may compriseindividually adding the perturbation vectors to the estimate and mappingthe result thereof.

The method may further comprise obtaining the estimate of the transmitsymbol vector provided by filtering a received vector.

The generating of the transmit symbol vector candidates may comprisesindividually adding the perturbation vectors to the estimate to obtaintransmit symbol vector estimates, and mapping the transmit symbol vectorestimates to a constellation symbol to generate the transmit symbolvector candidates.

The method may further comprise performing a hard decision decodingbased on the transmit symbol vector candidates.

The method may further comprise performing a soft decision decoding forreceived bits based on the transmit symbol vector candidates.

According to still another aspect, there is provided a method for use inan apparatus adopted to receive a signal transmitted in a communicationsystem, the method comprising generating perturbation vectors, andgenerating processed received vectors by perturbing a received vectorwith the perturbation vectors.

The generating of perturbation vectors may comprise randomly generatingvectors having a statistical nature corresponding tointerference-plus-noise on the received vector.

The generating of the processed received vectors may compriseindividually adding the perturbation vectors to the received vector.

The method may further comprise obtaining transmit symbol vectorestimates provided by filtering the processed received vectors.

The method may further comprise generating transmit symbol vectorcandidates by mapping the transmit symbol vector estimates to aconstellation symbol.

The method may further comprise generating transmit symbol vectorcandidates by perturbing at least a subset of the transmit symbol vectorestimates with post-perturbation vectors. The post-perturbation vectorsmay be randomly generated vectors that, on average, are contained withina sphere around a transmit symbol vector estimate.

The generating of the transmit symbol vector candidates may compriseindividually adding the at least the subset of the transmit symbolvector estimates to the post-perturbation vectors and mapping the resultthereof.

The generating of the transmit symbol vector candidates may comprisesgenerating post-transmit symbol vector estimates by individually addingthe at least the subset of the transmit symbol vector estimates to thepost-perturbation vectors, and generating the transmit symbol vectorcandidates by mapping the post-transmit symbol vector estimates to aconstellation symbol.

According to still another aspect, there is provided a computer-readablestorage medium storing a program for implementing a method for use in anapparatus adopted to receive a signal transmitted in a communicationsystem, the method comprising generating perturbation vectors, andgenerating transmit symbol vector candidates by perturbing an estimateof a transmit symbol vector with the perturbation vectors.

According to still another aspect, there is provided a computer-readablestorage medium storing a program for implementing a method for use in anapparatus adopted to receive a signal transmitted in a communicationsystem, the method comprising generating perturbation vectors, andgenerating processed received vectors by perturbing a received vectorwith the perturbation vectors. The method may further comprise obtainingtransmit symbol vector estimates provided by filtering the processedreceived vectors, and generating transmit symbol vector candidates byperturbing at least a subset of the transmit symbol vector estimateswith post-perturbation vectors.

Other features will become apparent to those skilled in the art from thefollowing detailed description, which, taken in conjunction with theattached drawings, discloses exemplary embodiments of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a configuration diagram illustrating an exemplary multiuserMIMO system utilizing a decoder and/or decoding method according to anexemplary embodiment.

Throughout the drawing and the detailed description, the same drawingreference numerals will be understood to refer to the same elements,features, and structures.

DETAILED DESCRIPTION

The following detailed description is provided to assist the reader ingaining a comprehensive understanding of the apparatuses, methods andsystems described herein. Accordingly, various changes, modifications,and equivalents of the systems, apparatuses and methods described hereinwill be suggested to those of ordinary skill in the art. Also,descriptions of well-known functions and constructions are omitted toincrease clarity and conciseness.

Decoders, apparatuses and/or methods consistent with the disclosures andteachings provided herein may be applied to a variety of known or to beknown communication system including a MIMO communication system such asa MIMO wireless communication system and a MIMO wire line communicationsystem, single-input multiple-output (SIMO) communication system,multiple-input single-output (MISO) communication system, cooperativeMIMO system, and the like. As an illustration, and without limitingthereto, a MIMO wireless communication system may include a single-userMIMO wireless system and a multiple-user MIMO wireless system. As anillustration, and without limiting thereto, a MIMO wire linecommunication system may include a digital subscriber line (DSL) systemsuch as a gigabit DSL system based on binder MIMO channels. Thedisclosures and teachings provided herein may also be applied to and/oradopted by various known and to be known standards and/or standardsetting organizations including, and without limiting thereto, IEEE802.x standards, worldwide interoperability for microwave access (WiMAX)broadband mobile standards, 3G mobile standards, mobile radio telephonestandards such as 3GPP and 3GPP2 standards, long term evolution (LTE)standards, wireless broadband (WiBro) standards, wideband code divisionmultiple access (WCDMA) standards, high-speed packet access plus (HSPA+)standards, and the like. Accordingly, a system/channel model describedbelow is only exemplary. In it a multiple-user communication system isconsidered, which subsumes a single-user point-to-point MIMO channel.

FIG. 1 illustrates an exemplary MU-MIMO system 100 comprising a basestation 110 and users 140. It is understood that a base station (or anaccess point) and a user may refer to a transmitter and a receiver,respectively, for downlink environments, whereas the base station andthe user may refer to a receiver and a transmitter, respectively, foruplink environments. It is also understood that, while not illustratedin FIG. 1, a receiver/transmitter may comprise a detector to detect asignal transmitted in the MU-MIMO system 100, transmitter unit, receiverunit, and/or transceiver unit, as the cases may be, and a processorand/or decoder that carries out a decoding method and/or algorithmaccording to certain exemplary embodiments disclosed herein. As anillustration, and without limiting thereto, a receiver/transmitter maybe a mobile/cellular phone, personal digital assistant (PDA), portablecomputer, portable media player (PMP), and the like, and as the casesmay be, may be an access point (AP), base station, terminal, router, andthe like. As an illustration, and without limiting thereto, a decodermay be implemented by hardware and/or software using known or to beknown methods and comprise one or more modules adopted to carry out adecoding method and/or algorithm according to certain exemplaryembodiments disclosed herein. It is understood and within one skilled inthe art that, for example, operations carried out by several modules maybe adopted to be carried out by one equivalent module and vice versa.

FIG. 1 shows both uplink and downlink transmissions. In downlinktransmission, the base station 110 may transmit to multiple users 140simultaneously. In uplink transmission, multiple users 140 may transmitsimultaneously to the base station 110. Referring to FIG. 1, consider adownlink of a multiuser channel for which the base station 110 isequipped with N_(T) transmit antennas which communicate with L users140. User l, l=1, . . . , L, is equipped with N_(R) _(l) receiveantennas. A notation {N_(R) ₁ , N_(R) ₂ , . . . , N_(R) _(L) }×N_(T) maybe used to refer to such a channel. A received signal at user l may bemodeled by the following input-output relation

$\begin{matrix}{{Y_{l} = {{\sqrt{\frac{E_{s}}{N_{T}}}H_{l}^{act}W_{l}S_{l}} + {\underset{i \neq l}{\sum\limits_{i = 1}^{L}}{H_{l}^{act}W_{i}S_{i}}} + V_{l}}},} \\{= {{\sqrt{\frac{E_{s}}{N_{T}}}H_{l}\underset{\_}{S}} + {V_{l}.}}}\end{matrix}$

Where L≦N_(T) and H_(l)=H_(l) ^(act)W is the effective channel matrixfor user l. It is derived by the use of a unitary precoder matrix,W=[W₁, . . . , W_(L)], on the actual channel matrix for user l, H_(l)^(act). S=[S₁ ^(T), . . . , S_(L) ^(T)]^(T) is the N_(T)×1 symbol vectortransmitted to users 140 from the base station 110, such that E{S}=0 andE{S*S}=N_(T). Let each element of S be drawn independently from acomplex constellation C. V_(l) is additive white Gaussian noiseCN(0,I_(N) _(Rl) ). It may be assumed that user l has no knowledge ofthe channel matrix from the base station 110 to any other user.

Various precoder design techniques for W have been investigated. In a ZFprecoding method in e.g., Q. H. Spencer, A. L. Swindledurst, and M.Haardt, “Zero-forcing methods for downlink spatial multiplexing inmultiuser MIMO channels,” IEEE Trans. on Signal Processing,52(2):461-471, February 2004, the reference of which is incorporatedherein by reference in its entirety for all purposes, a blockdiagonalization (BD) algorithm is considered. With this approach, fulltransmitter channel side information (CSIT) for all users is assumed.The precoder for each user is selected so that it may fall within thenull space of every other users channel matrix. In theory, allmulti-user interference is eliminated for all users in the system, andthe resulting channel is equivalent in performance to a point-to-pointMIMO channel (i.e., single user).

In reality, it is difficult for a base station to have perfect CSIT dueto the delayed and lossy characteristics of a feedback link. In thiscase, precoders W_(l) could be chosen as in e.g., D. J. Love, R. W.Heath, and T. Strohmer, “Grassmanian beamforming for multiple-inputmultiple-output wireless systems,” IEEE Trans. on Information Theory,49(10):2735-2747, October 2003, the reference of which is incorporatedherein by reference in its entirety for all purposes, from a finite setcodebook, where the codebook is designed using a Grassmannian linepacking. In addition, user scheduling and antenna selection may be usedto obtain additional achievable throughput, as in e.g., S. J. Kim, H.Kim, C. S. Park, and K. B. Lee, “On the performance of multiuser MIMOsystems in WCDMA/HSDPA: Beamforming, feedback and user diversity,” IEICETrans. on Communications, E89-B(8):2161-2169, August 2006 and R. W.Heath, M. Airy, and A. J. Paulraj, “Multiuser diversity for MIMOwireless systems with linear receivers,” IEEE Communications Letters,5(4):142-144, April 2001, the references of which are incorporatedherein by reference in its entirety for all purposes. This is achievedby the use of a multiuser MIMO scheme that is called a per-user unitarybeamforming and rate control (PU2RC). Here, the constraint placed on Wmay be such that W*W=I_(N) _(T) .

Certain embodiment including decoders and decoding methods according toexemplary embodiments are further disclosed below.

Post-Perturbed Decoder and Decoding Method

A post-perturbed decoder according to an exemplary embodiment may beused for, for example, either a full feedback or a limited feedback.According to an aspect, the post-perturbed decoder, which may also bereferred to as a post-perturbed sphere-like decoder, aims to achieve aperformance edge over linear filters such as ZF and MMSE decoders inSU-MIMO systems and for uplink and down link transmissions in MU-MIMOsystems. As taught herein, the complexity of the post-perturbed decoderis less than that of a ML decoder which requires an exhaustive search. Alist of possible transmit symbol vector candidates provided by thepost-perturbed decoder may be used for a hard decision using, forexample, a minimum distance decoding. The list may also be used for asoft decision decoding for which the performance may be further improvedby the use of an outer channel code. An exemplary method of generatingthe list is described below.

According to an aspect, the post-perturbed decoder attempts to find a MLestimate from an estimate of a transmit symbol vector. This is achievedby perturbing a transmit symbol vector estimate, that is, an estimate ofa transmit symbol vector, with randomly generated vectors that, onaverage, are contained within a sphere around the estimate provided by alinear decoder. Linear decoders such as ZF and MMSE decoder may be usedon a received vector to compute the transmit symbol vector estimate. Therandomly generated vectors are individually added to this estimate andmapped to form a list of possible transmit symbol vector candidates.According to another aspect, based on the list, a minimum distancedecoding may be performed as in the case of a ML or soft information ontransmitted bits may be generated.

The decoder according to an exemplary embodiment generates Kperturbation vectors and forms a set P={P₀, P₁, . . . , P_(K)}, suchthat P₀ is the all zeros vector. The perturbation vectors may begenerated as random vectors with statistical nature such that on averagethey fit within a sphere around an estimate. For example, to fit withina sphere of radius √{square root over (E_(P))} around the estimate, thevectors may be generated as CN(0, E_(P)I_(N) _(T) ).

For each user, a received vector Y_(l) is processed by a linear filterto obtain an estimate of the transmit symbol vector, Z_(est).

Z_(est)=GY_(l).

Where Gε{G_(ZF), G_(MMSE)} is either a ZF or MMSE decoding matrix. Thisestimate is individually added to the perturbation vectors to form a setZ={Z₀, . . . , Z_(K)}. Where,

Z _(k) =Z _(est) +P _(k) for k=0, . . . , K.

Each element in Z is mapped to the closest constellation symbol in C.This mapping creates a set of possible transmit symbol vectorcandidates, Ŝ={Ŝ₀, Ŝ₁, . . . , Ŝ_(K)}, such that

${\hat{S}}_{k} = {{{map}\mspace{11mu} ( Z_{k} )} = {{{\begin{bmatrix}{{map}\mspace{11mu} ( z_{k,1} )} \\{{map}\mspace{11mu} ( z_{k,2} )} \\\vdots \\{{map}\; ( z_{k,N_{T}} )}\end{bmatrix}.{Where}}\mspace{14mu} {{map}(z)}} = {\underset{s \in C}{\arg \; \min}{{{z - s}}^{2}.}}}}$

Some transmit symbol vector estimates, Z_(k), might map into the sametransmit symbol vector candidates in Ŝ. Thus,

Ŝ={Ŝ₀,Ŝ₁, . . . , Ŝ_(M)} M≦K.

This list of possible transmit symbol vector candidates may be used as asearch space for a hard maximum likelihood decision. In this case, theoutput of the post-perturbed decoder, Ŝ_(l) ^(PPD) may be calculated as

${\hat{S}}_{l}^{PPD} = {\underset{{m = 1},\mspace{14mu} \ldots \mspace{14mu},M}{\arg \; \min}{{{Y - {\sqrt{\frac{E_{s}}{N_{T}}}H_{l}{\hat{S}}_{m}}}}^{2}.}}$

The list may also be used to provide soft information on bits that makeup the transmitted symbol vector. Hence, a soft decision decoding may beperformed on received bits. The performance of the decoder may befurther improved by using it in concatenation with an “outer” channelcode, e.g., a convolutional code, turbo code and the like. The softinformation may computed as a log-likelihood ratio (LLR) which is givenby

${{LLR}( {bit}_{i} )} = {\ln( \frac{\sum\limits_{X \in {\hat{S}}_{i,1}}{{Y_{l} - {\sqrt{\frac{E_{s}}{N_{T}}}H_{l}X}}}^{2}}{\sum\limits_{X \in {\overset{\sim}{S}}_{i,0}}{{Y_{l} - {\sqrt{\frac{E_{s}}{N_{T}}}H_{l}X}}}^{2}} )}$

Where {tilde over (S)}_(i,1) is the subset of Ŝ that contains symbolvectors that have a “1” in the i^(th) bit position and {tilde over(S)}_(i,0) is the subset of Ŝ that contains symbol vectors that have a“0” in the i^(th) bit position.

A post-perturbed decoder algorithm according to an exemplary embodimentis described below.

Obtain a transmit symbol vector estimate, Z_(est), by the use of alinear decoder.

Z_(est) = GY_(l).Where  G ∈ {G_(ZF), G_(MMSE)} and$G_{ZF} = {{( {H_{l}^{*}H_{l}} )^{- 1}{H_{l}^{*}.G_{MMSE}}} = {\lbrack {{H_{l}^{*}H_{l}} + {\frac{N_{T}}{E_{s}}I_{N_{T}}}} \rbrack^{- 1}{H_{l}^{*}.}}}$

Generate K random perturbation vectors, P={P₀, P₁, . . . , P_(K)} suchthat P₀ is the all zeros vector.

Create a set of transmit symbol vector estimates by perturbing Z_(est)with the vectors in P.

Z _(k) =Z _(est) +P _(k).

Generate a list Ŝ={Ŝ₀,Ŝ₁, . . . , Ŝ_(M)}, such that Ŝ_(m)=map(Z) m=1, .. . , M≦K.

Perform a maximum likelihood “hard” decoding or a “soft” decoding fromthe list Ŝ.

The performance of the post-perturbed decoder may be dependent on thenumber of perturbation vectors, K, which in turn determines the size ofthe list of possible transmit symbol vector candidates. Eachperturbation vector may not map in a one-to-one pattern to transmitsymbol vectors. Some of the perturbations may map to the same uniquetransmit symbol vector. Accordingly, the size of the eventual list oftransmit symbol vector candidates is usually less than the number ofperturbation vectors used.

Pre-Perturbed Decoder and Decoding Method

A pre-perturbed decoder according to an exemplary embodiment may be usedfor, for example, either a full feedback or a limited feed-back.According to an aspect, statistics, e.g., mean and variance, ofinterference-plus-noise may be known at a receiver. And thepre-perturbed decoder attempts to mitigate the effect ofinterference-plus-noise on a transmitted signal vector at the receiver.This is achieved by perturbing a received signal with randomly generatedvectors that have the same statistics as the unknowninterference-plus-noise. According to another aspect, linear decoderssuch as ZF and MMSE decoders may used on the pre-processed perturbedvectors to compute the possible transmit symbol vector candidates.Accordingly, a minimum distance decoding may be performed as in the caseof the ML or soft information on transmitted bits may be generated.

The decoder according to an exemplary embodiment generates Kperturbation vectors and forms a set {tilde over (P)}={P₀, . . . ,P_(K)}, such that P₀ is the all zeros vector. The perturbation vectorsmay be generated as random vectors with the same statistical nature asthe interference-plus-noise. For example, in a point-to-point MIMOsystem with a single user, the elements of {tilde over (P)} are CN(0,I_(N) _(T) ). However in the multiuser case, the elements of {tilde over(P)} are CN(0, σ²), where σ² is the variance of theinterference-plus-noise component.

A received vector Y is pre-processed by individually adding to it theperturbation vectors P₀, . . . , P_(K) and forming a set {tilde over(Y)}={Y₀, . . . , Y_(K)}, that is, processed received vectors.

Y _(k) =Y+P _(k), k=0, . . . , K.

In this case, for example, ZF and MMSE linear receivers may be used forwhich

G_(ZF) = [H_(l)^(*)H_(l)]⁻¹H_(l)^(*) and$G_{MMSE} = {\lbrack {{H_{l}^{*}H_{l}} + {\frac{N_{T}}{E_{s}}I_{N_{T}}}} \rbrack^{- 1}{H_{l}^{*}.}}$

For either choice of linear receiver, a set of transmit symbol vectorestimates Z_(k)=GY_(k), k=0, . . . , K, is formed. Where Gε{G_(ZF),G_(MMSE)}.

Each element in each symbol vector is mapped to the closestconstellation symbol. This mapping creates a set of possible transmitsymbol vector candidates, {tilde over (S)}.

${\overset{\sim}{S}}_{k} = {{{map}( Z_{k} )} = \begin{bmatrix}{{map}( z_{k,1} )} \\{{map}( z_{k,2} )} \\\vdots \\{{map}( {z_{k},N_{T}} )}\end{bmatrix}}$${{Where}\mspace{14mu} {{map}(z)}} = {\underset{s \in C}{\arg \; \min}{{{z - s}}^{2}.}}$

Some transmit symbol vector estimates, Zk, might map into the sametransmit symbol vector candidates in {tilde over (S)}. Thus, {tilde over(S)}={{tilde over (S)}₁, . . . , {tilde over (S)}_(M)}, M≦K. This listof possible symbol vector candidates may be used as a search space for ahard maximum likelihood decision. In this case, the output of thepre-perturbed decoder, {tilde over (S)}_(PPD), may be calculated as

${\hat{S}}_{l}^{PPD} = {\underset{{m = 1},\mspace{14mu} \ldots \mspace{14mu},M}{\arg \; \min}{{{Y - {\sqrt{\frac{E_{S}}{N_{T}}}H_{l}{\overset{\sim}{S}}_{m}}}}^{2}.}}$

In a single-user scenario, the list may also be used to create softinformation on bits that make up the transmitted symbol vector. Hence, asoft decision decoding may be performed on received bits. Theperformance of the decoder may be further improved by using it inconcatenation with an “outer” channel code, e.g., a convolutional code,turbo code and the like. The soft information may be computed as alog-likelihood ratio (LLR) which is given by

${{LLR}( {bit}_{i} )} = {{\ln( \frac{\sum\limits_{X \in {\overset{\sim}{S}}_{i,1}}{{Y_{l} - {H_{l}^{act}X}}}_{2}^{2}}{\sum\limits_{X \in {\overset{\sim}{S}}_{i,0}}{{Y_{l} - {H_{l}^{act}X}}}_{2}^{2}} )}.}$

Where {tilde over (S)}_(i,1) is the subset of {tilde over (S)} thatcontains symbol vectors that have a “1” in the i^(th) bit position and{tilde over (S)}_(i,0) is the subset of {tilde over (S)} that containssymbol vectors that have a “0” in the i^(th) bit position.

A pre-perturbed decoder algorithm according to an exemplary embodimentis described below.

Generate K random perturbation vectors, P₁, . . . , P_(K).

Form a set {tilde over (P)}={P₀, P₁, . . . , P_(K)} such that P₀ is theall zeros vector.

Create a set of processed received vectors, {tilde over (Y)}={Y₀, . . ., Y_(K)} by perturbing Y with the vectors in {tilde over (P)}. Where,Y_(k)=Y+P_(k). k+0, . . . , K.

Use a linear decoder on the vectors in {tilde over (Y)} to create a listof transmit symbol vector estimates, Z_(k). Z_(k)=GY_(k). k=0, . . . ,K. Where Gε{G_(ZF), G_(MMSE)}.

Generate a list {tilde over (S)}={{tilde over (S)}₁, . . . , {tilde over(S)}_(M)}, such that {tilde over (S)}_(m)=map(Z), m=1, . . . , M≦K. Itis possible that some estimates will map to the same transmit symbolvector.

Perform a maximum likelihood (ML) decoding or a soft decoding over{tilde over (S)}.

The performance of the pre-perturbed decoder may be dependent on thenumber of perturbation vectors, K, which in turn determines the size ofthe list of possible transmit symbol vector candidates. Eachperturbation vector may not map in a one-to-one pattern to transmitsymbol vectors. Some of the perturbations may map to the same uniquetransmit symbol vector. Accordingly, the size of the eventual list oftransmit symbol vector candidates is usually less than the number ofperturbation vectors used.

Dual-Perturbed Decoder and Decoding Method

A dual-perturbed decoder according to an exemplary embodiment may beused for, for example, either a full feedback or a limited feedback.According to an aspect, the dual-perturbed decoder aims to achieve aperformance edge over linear filters such as ZF and MMSE decoders inSU-MIMO systems and for uplink and down link transmissions in MU-MIMOsystems. As taught herein, the complexity of the dual-perturbed decoder,which may also be referred to as a dual-perturbed sphere-like decoder,is less than that of a ML decoder which requires an exhaustive search. Alist of possible transmit symbol vector candidates provided by thedual-perturbed decoder, may be used for a hard decision, for example,using a minimum distance decoding. The list may also be used for a softdecision decoding for which the performance may be further improved bythe use of an outer channel code. An exemplary method of generating thislist is described below.

According to an aspect, the dual-perturbed decoder attempts to find a MLestimate by a combination of pre-processing, and post-processing ofestimates obtained by a linear decoder. Pre-processing may be achievedby perturbing a received signal to prevent interference and noise.Post-processing may be achieved by perturbing the estimates obtainedfrom pre-processing with randomly generated vectors that, on average,are contained within a sphere around the estimate provided by a lineardecoder.

A received signal vector may be processed by randomly generatedpre-perturbation vectors. The result of each perturbation is fed into alinear decoder such as a ZF decoder or a MMSE decoder. These decodersmay provide a transmit symbol vector estimate for each perturbation. Therandomly generated post-perturbation vectors are individually added tothese estimates and mapped to form a list of possible transmit symbolvector candidates. Accordingly, a minimum distance decoding may beperformed as in the case of the ML or soft information on transmittedbits may be generated.

The decoder according to an exemplary embodiment generates K₁pre-perturbation vectors and forms a set P₁={P_(1,0), P_(1,1), . . . ,P_(1,K) ₁ }, such that P_(1,0) is the all zeros vector. P_(1,k) ₁ εC^(N)^(Rl) is generated such that it has the same statistical characteristicsas the interference-plus-noise. Post-perturbation vectors, P₂={P_(2,0),P_(2,1), . . . , P_(2,K) ₁ }, are also generated as random vectors withstatistical nature such that on average they fit within a sphere arounda transmit symbol vector estimate. For example, to fit within a sphereof radius √{square root over (E_(P))} around the estimate, the vectorscould be generated as CN(0, E_(p)I_(N) _(T) ).

For each user, a received vector Y_(l), is pre-processed by individuallyperturbing by the vectors in P₁. This forms a set Y={Y₀, . . . , Y_(K) ₁} such that

Y _(k) ₁ =Y _(l) +P _(1,k) ₁ . k₁=0,2, . . . , K₁.

Each perturbed vector in Y is processed by a linear filter to obtain anestimate of the transmit symbol vector. This list of transmit symbolvector estimates Z is generated such that.

Z={Z_(k) ₁ :Z_(k) ₁ =GY_(k) ₁ }.

Where Gε{G_(ZF), G_(MMSE)} is either a ZF or MMSE decoding matrix. Eachestimate in Z is individually added to the post-perturbation vectors,P₂, to form the set {circumflex over (Z)}={{circumflex over (Z)} ₀,{circumflex over (Z)} ₁, . . . , {circumflex over (Z)} _(K) ₂ }, thatis, post-transmit symbol vector estimates. Where,

{circumflex over (Z)} _(k) ₂ ={{circumflex over (Z)} _(k) ₁ _(,k) ₂:{circumflex over (Z)} _(k) ₁ _(,k) ₂ =Z _(k) ₁ +P _(2,k) ₂ } for k₁=0,. . . , K₁ and k₂=0, . . . , K₂.

Each element in {circumflex over (Z)} is mapped to the closestconstellation symbol in C. This mapping creates a set of possibletransmit symbol vector candidates, Ŝ={Ŝ₀, Ŝ₁, . . . , Ŝ_(K)}, such that

${\hat{S}}_{k} = {{{map}\mspace{11mu} ( {\hat{Z}}_{k} )} = {{{\begin{bmatrix}{{map}\mspace{11mu} ( {\hat{z}}_{k,1} )} \\{{map}\mspace{11mu} ( {\hat{z}}_{k,2} )} \\\vdots \\{{map}\; ( {\hat{z}}_{k,N_{T}} )}\end{bmatrix}.{Where}}\mspace{14mu} {{map}(z)}} = {\underset{s \in C}{\arg \; \min}{{{z - s}}^{2}.}}}}$

This list of possible symbol vector candidates may be used as a searchspace for a hard maximum likelihood decision. In this case, the outputof the dual-perturbed decoder, Ŝ_(l) ^(DP), may be calculated as

${\hat{S}}_{l}^{DP} = {\underset{{\hat{S}}_{m} \in \hat{S}}{\arg \; \min}{{{Y_{l} - {\sqrt{\frac{E_{s}}{N_{T}}}H_{l}{\hat{S}}_{m}}}}^{2}.}}$

The list may also be used to create soft information on bits that makeup the transmitted symbol vector. Hence, a soft decision decoding may beperformed on received bits. The performance of the decoder may beimproved by using it in concatenation with an “outer” channel code,e.g., a convolutional code, turbo code and the like. The softinformation may be computed as a log-likelihood ratio (LLR) which isgiven by

${{LLR}( {bit}_{i} )} = {\ln( \frac{\sum\limits_{X \in {\overset{\sim}{S}}_{i,1}}{{Y_{l} - {\sqrt{\frac{E_{s}}{N_{T}}}H_{l}X}}}^{2}}{\sum\limits_{X \in {\overset{\sim}{S}}_{i,0}}{{Y_{l} - {\sqrt{\frac{E_{s}}{N_{T}}}H_{l}X}}}^{2}} )}$

Where {tilde over (S)}_(i,1) is the subset of Ŝ that contains symbolvectors that have a “1” in the i^(th) bit position and {tilde over(S)}_(i,0) is the subset of Ŝ that contains symbol vectors that have a“0” in the i^(th) bit position.

A dual-perturbed decoder algorithm according to an exemplary embodimentis described below.

Generate a set of pre-perturbed vectors, P₁={P_(1,0), P_(1,1), . . . ,P_(1,K) ₁ }.

Create a list Y={Y₀, . . . , Y_(K) ₁ } by pre-processing a receivedsignal, Y_(l), such that

Y _(k) ₁ =Y _(l) +P _(1,k) ₁ for k₁=0,1, . . . , K₁.

Obtain a transmit symbol vector estimate for each vector in Y by the useof a linear decoder. Let this list be

$\underset{\_}{Z} = {{{\{ {{Z_{k}\text{:}Z_{k}} = {GY}_{k}} \}.{Where}}\mspace{14mu} G} \in {\{ {G_{ZF},G_{MMSE}} \} \mspace{20mu} {and}}}$$G_{ZF} = {{\lbrack {( {H_{l}H_{l}^{*}} )^{- 1}H_{l}} \rbrack^{*}.G_{MMSE}} = {\lbrack {( {{H_{l}H_{l}^{*}} + {\frac{N_{T}}{E_{s}}I_{N_{R_{l}}}}} )^{- 1}H_{l}} \rbrack^{*}.}}$

Generate K₂ random vectors, that is, post-perturbation vectorsP₂={P_(2,0), P_(2,1), . . . , P_(2,K) ₂ } such that P_(2,0) is the allzeros vector.

Create a set of transmit symbol vector estimates, that is, post-transmitsymbol vector estimates, by perturbing Z with vectors in P₂. Thispost-perturbed list {circumflex over (Z)}={{circumflex over (Z)} ₀,{circumflex over (Z)} ₁, . . . , {circumflex over (Z)} _(K) ₂ } iscreated such that

{circumflex over (Z)} _(k) ₂ ={{circumflex over (Z)} _(k) ₁ _(,k) ₂:{circumflex over (Z)} _(k) ₁ _(,k) ₂ =Z _(k) ₁ +P _(2,k) ₂ }.

Generate a list Ŝ={Ŝ₀, Ŝ₁, . . . , Ŝ_(M)}, such that

Ŝ_(m)=map({circumflex over (Z)}) m=1, . . . , M≦K₁K₂.

Perform a maximum likelihood “hard” decoding or a “soft” decoding fromthe list Ŝ.

The performance of the dual-perturbed decoder may be dependent on thenumber of perturbation vectors, K₁ and K₂, which in turn determines thesize of the list of possible transmit symbol vector candidates. Eachperturbation vector may not map in a one-to-one pattern to transmitsymbol vectors. Some of the perturbations may map to the same uniquetransmit symbol vector. Accordingly, the size of the eventual list oftransmit symbol vector candidates is usually less than the number ofperturbation vectors used.

Without a list constraint, the size of the dual-perturbed transmitsymbol vector estimate list may grow as large as K₁K₂, which maysometimes be redundant since it may be as large as an exhaustive search.Accordingly, according to another aspect, the list size may beconstrained after the pre-processing. This may be achieved by, forexample, picking a subset with the most reliable estimates after thepre-processing. Post-perturbing may be provided with respect to thevectors in this subset. For example, 10 closest transmit symbol vectorestimates may be chosen after a pre-perturbation, and post-perturbationmay be performed on this subset.

The methods described herein including the post-perturbed,pre-perturbed, and dual-perturbed decoding method and the correspondingalgorithms may be recorded, stored, or fixed in one or morecomputer-readable media that includes program instructions to beimplemented by a computer to cause a processor to execute or perform theprogram instructions. The media may also include, alone or incombination with the program instructions, data files, data structures,and the like. Examples of computer-readable media include magneticmedia, such as hard disks, floppy disks, and magnetic tape; opticalmedia such as CD ROM disks and DVDs; magneto-optical media, such asoptical disks; and hardware devices that are specially configured tostore and perform program instructions, such as read-only memory (ROM),random access memory (RAM), flash memory, and the like. The media mayalso be a transmission medium such as optical or metallic lines, waveguides, and the like including a carrier wave transmitting signalsspecifying the program instructions, data structures, and the like.Examples of program instructions include both machine code, such asproduced by a compiler, and files containing higher level code that maybe executed by the computer using an interpreter. The described hardwaredevices may be configured to act as one or more software modules inorder to perform the operations and methods described above.

According to certain embodiments described above, decoders are providedthat may improve the performance of linear decoders such as ZF and MMSEdecoders. According to an aspect, the complexity of the decoder is lessthan is typically required for an exhaustive search in a ML decoding.However, the performance of the decoders may generally be better thanthe performance of using only the linear decoders.

It is understood that the terminology used herein, for example, atransmit symbol vector and perturbed, may be different in otherapplications or when described by another one skilled in the art.

A number of exemplary embodiments have been described above.Nevertheless, it will be understood that various modifications may bemade. For example, suitable results may be achieved if the describedtechniques are performed in a different order and/or if components in adescribed system, architecture, device, or circuit are combined in adifferent manner and/or replaced or supplemented by other components ortheir equivalents. Accordingly, other implementations are within thescope of the following claims.

1. A decoder adopted to receive a signal transmitted in a communicationsystem, the decoder comprising: a module adopted to provide perturbationvectors; and a module adopted to provide transmit symbol vectorcandidates by perturbing an estimate of a transmit symbol vector withthe perturbation vectors.
 2. The decoder of claim 1, wherein thecommunication system is a multiple-input multiple-output (MIMO)communication system.
 3. The decoder of claim 1, wherein theperturbation vectors are randomly generated vectors that, on average,are contained within a sphere around the estimate.
 4. The decoder ofclaim 1, wherein the perturbation vectors are individually added to theestimate and the result mapped to provide the transmit symbol vectorcandidates.
 5. The decoder of claim 1, further comprising a moduleadopted to provide the estimate of the transmit symbol vector byfiltering a received vector.
 6. The decoder of claim 1, wherein themodule adopted to provide the transmit symbol vector candidatescomprises: a module adopted to provide transmit symbol vector estimatesby individually adding the perturbation vectors to the estimate; and amodule adopted to provide the transmit symbol vector candidates bymapping the transmit symbol vector estimates to a constellation symbol.7. The decoder of claim 1, further comprising a module adopted toperform a hard decision decoding based on the transmit symbol vectorcandidates.
 8. The decoder of claim 1, further comprising a moduleadopted to perform a soft decision decoding for received bits based onthe transmit symbol vector candidates.
 9. The decoder of claim 1,wherein a number of the transmit symbol vector candidates is less thanthat of the perturbation vectors.
 10. A decoder adopted to receive asignal transmitted in a communication system, the decoder comprising: amodule adopted to provide perturbation vectors; and a module adopted toprovide processed received vectors by perturbing a received vector withthe perturbation vectors.
 11. The decoder of claim 10, furthercomprising a module adopted to provide transmit symbol vector estimatesby filtering the processed received vectors.
 12. The decoder of claim11, further comprising a module adopted to provide transmit symbolvector candidates by perturbing at least a subset of the transmit symbolvector estimates with post-perturbation vectors.
 13. A method for use inan apparatus adopted to receive a signal transmitted in a communicationsystem, the method comprising: generating perturbation vectors; andgenerating transmit symbol vector candidates by perturbing an estimateof a transmit symbol vector with the perturbation vectors.
 14. A methodfor use in an apparatus adopted to receive a signal transmitted in acommunication system, the method comprising: generating perturbationvectors; and generating processed received vectors by perturbing areceived vector with the perturbation vectors.
 15. The method of claim14, wherein the generating of perturbation vectors comprises randomlygenerating vectors having a statistical nature corresponding tointerference-plus-noise on the received vector.
 16. The method of claim14, wherein the generating of the processed received vectors comprisesindividually adding the perturbation vectors to the received vector. 17.The method of claim 14, further comprising obtaining transmit symbolvector estimates provided by filtering the processed received vectors.18. The method of claim 17, further comprising generating transmitsymbol vector candidates by mapping the transmit symbol vector estimatesto a constellation symbol.
 19. The method of claim 18, furthercomprising performing one of a hard decision decoding and a softdecision decoding for received bits, based on the transmit symbol vectorcandidates.
 20. The method of claim 17, further comprising generatingtransmit symbol vector candidates by perturbing at least a subset of thetransmit symbol vector estimates with post-perturbation vectors.
 21. Themethod of claim 20, wherein the post-perturbation vectors are randomlygenerated vectors that, on average, are contained within a sphere arounda transmit symbol vector estimate.
 22. The method of claim 20, whereinthe generating of the transmit symbol vector candidates comprisesindividually adding the at least the subset of the transmit symbolvector estimates to the post-perturbation vectors and mapping the resultthereof.
 23. The method of claim 20, wherein the generating of thetransmit symbol vector candidates comprises: generating post-transmitsymbol vector estimates by individually adding the at least the subsetof the transmit symbol vector estimates to the post-perturbationvectors; and generating the transmit symbol vector candidates by mappingthe post-transmit symbol vector estimates to a constellation symbol. 24.An apparatus for receiving and/or transmitting a signal in amultiple-input multiple-output (MIMO) communication system, theapparatus comprising: a detector; and a decoder comprising one or moreof: a module adopted to pre-process a received signal to reduce theeffect of interference-plus-noise on the received signal beforefiltering the received signal, and a module adopted to post-process theresult of filtering the received signal.
 25. The apparatus of claim 24,wherein the module adopted to post-process provides transmit symbolvector candidates by perturbing the result with perturbation vectors.